On the unramified Eisenstein spectrum

Abstract

For a split reductive group ${}^{L}G$ over a global field, we determine the spectrum of the spherical Hecke algebra coming from the unramified Eisenstein series for the minimal parabolic ${}^{L}B$. This is done using a certain decomposition of the Springer stack $T^{\ast }(B\backslash G/B)$ for the Langlands dual group in the additive group of cobordisms of cohomologically proper derived quotient stacks.

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